on enders free time, he plays the mind game and kills the giant. later ender starts to avoid the game, which reveals peter on the screen. we learn that the program self-generates ideas from ender's life.
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Ender's brother Peter has always been an antagonist in his life. Peter represents everything that Ender doesn't want to become (violent, socio-path...) Killing the giant was a violent act. Ender is thrust into a world of violence yet he doesn't want to become violent himself. Peter is a manifestation of Ender's own fears of becoming like his brother.